A network engineer studies the operation of a data communication system. To do this, it collects information on how the data is served on the different devices in the system. The data communication system has a waiting queue. The data arrives at the data communication system with an interarrival time that is distributed exponentially, with an average of $6$ minutes.

There are two access devices to first classify the data. Access device A classifies $60\%$ of the incoming data and access device B the remaining $40\%.$

We know that once the data has been entered:

to$.$ to access device A$,$ has a probability of:

Yo$.0\mathrm{.}2$ of going to data device C and then logging out

ii$.0\mathrm{.}8$ to go to data device D and then

$1.0\mathrm{.}6$ go to data device E and then log out

$2.0\mathrm{.}4$ go to data device F and then log out

b$.$ data device B$,$ has a probability of:

Yo$.1$ of going to data device F and then logging out

All devices process data with an average of $4$ minutes. Determine:

a$)$ The average number of data waiting in the queue on data device A$.$

b$)$ The average time that data passes from when it enters the data communication system until it leaves it$.$